Question

The Kangaroo Lodge of Madison County has 10 members (A, B, C, D, E, F, G, H, I, and J). The club has five working committees: the Rules Committee (A, C, D, E, I, and I), the Public Relations Committee (B, C, D, H, I, and J), the Guest Speaker Committee (A, D, E, F, and H), the New Year's Eve Party Committee (D, F, G, H, and I), and the Fund Raising Committee (B, D, F, H, and J). (a) Suppose we are interested in knowing which pairs of members are on the same committee. Draw a graph that models this problem. (Hint: Let the vertices of the graph represent the members.) (b) Suppose we are interested in knowing which commit- tees have members in common. Draw a graph that models this problem. (Hint: Let the vertices of the graph represent the committees.)

Answer 1

To answer this question, we can draw two graphs: one to represent the pairs of members on the same committee and another to represent the committees that have members in common.

(a) To draw a graph that models the problem, we can use vertices to represent the members and edges to represent the pairs of members on the same committee. Here is the graph:

(b) To draw a graph that models the problem of which committees have members in common, we can use vertices to represent the committees and edges to represent the committees that share at least one member. Here is the graph:

Answer 2

If your saying hint, then shouldn’t you already know it? But whatever it’s A